ps11 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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M ASSACHUSETTS I NSTITUTE OF T ECHNOLOGY 15.053 – Optimization Methods in Management Science (Spring 2007) Problem Set 11, Due December 3 rd 2013 You will need 0 points out of 0 to receive a grade of 0 Prologue: Nooz, feeling he was promised an equal starring role in the course, and in the end taking a backseat to Ollie and Tim, decides to leave the course to pursue a few “real world jobs”. Will this sly fox make it in the real world and cease to exist as a 15.053 character or return to his role as our number one fox? In this problem set, we follow the adventures of Nooz while learning about our final topic decision analysis. Problem 1: Nooz Shakes the Steak Nooz’s Chicken Coop and Steak and Shake are two competing restaurants. Each must determine simultaneously whether to undertake small, medium, or large advertising campaigns. Nooz believes that it is equally likely that Steak and Shake will undertake a small, a medium, or a large advertising campaign. Given the actions chosen by each restaurant, Nooz’s profits are as shown below. Steak and Shake Chooses Nooz Chooses Small Medium Large Small 4,000 3,000 2,000 Medium 5,000 4,000 3,000 Large 6,000 5,000 1,500 Determine Nooz’s choice under the following decision criteria: Part A: maximin Part B: maximax Part C: minimax regret
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Part D: expected value (here, assume Steak and Shake’s three choices are equally likely.) Problem 2: Foxes and Fools Having lost the fast food battle; Nooz decides to start a new News station called Fox Nooz. The Fox Nooz station generates a profit of $5 million on average for a new show that becomes a hit, and loses $1 million on average for a show that is a failure. Of all shows that Fox Nooz is considering, they expect that 30% of them will be a hit and 70% will be a failure. For the cost of $500,000, the station can make a pilot that will indicate whether or not a show will be a hit or a failure. If the pilot is a hit, the series will be a hit with 100% probability. If the pilot is a failure, then with 100% probability it will be a failure. (In practice, pilots are not so reliable as indicators, and the numbers are chosen here to make the problem simpler.) Fox Nooz is thinking of producing the new reality series entitled, ‘Who Is the Biggest Fool: Bill Clinton or Turkey Tim?’. The show puts two Democrats against each other in a variety of clown-like challenges. Fox Nooz needs to decide whether or not to produce
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ps11 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY 15.053...

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